One type of logical deduction game requires a player to deduce a particular arrangement of game pieces selected by an opponent with provided clues. One currently popular logical game, MASTERMIND, described in Canadian Pat. No. 1,009,675, includes sets of pegs having different colors. A predetermined number of these pegs are arranged in a sequence on a pegboard by one player. A second player who is unable to see the pegs of the first player attempts to deduce the colors and sequence of the pegs in response to clues from the first player. Each clue follows each turn of the second player. Each turn requires the second player to display different colored pegs in a successive row of the pegboard. After each turn, the first player provides the second player with clues in the form of black and white pegs; a black peg informs the second player that one of the selected pegs is correct in color and pegboard position while a white peg informs that a correctly colored peg only has been chosen (i.e. not placed by the second player in a pegboard hole corresponding to the location of the first player's correspondingly colored peg). The first player's object is to determine the opponent's peg arrangement in the least number of turns with these clues. To my knowledge, only one player can play against an opponent, thus precluding others from participating. Also the game is limited to deduction of colors, although a variance of the game utilizing letters to form words is known.
Another numerical game, disclosed in British Pat. No. 1,541,537, includes several game cards, having sixteen numbers printed in a four-by-four matrix so the sum of the numbers is `34` in each of the horizontal, vertical and diagonal directions. The game cards are not identical since either different numbers are used to obtain the sum of `34` or the same number appearing in more than one game card may appear in a different row or column in different game cards. One of the players who is a dealer selects one of the game cards and hides it from the view of the other player. The object of the game is for the other player to determine the correct location of the game card numbers with clues supplied by throwing three dice and having the dealer position a numbered peg corresponding to the sum of the three dice in a peg hole on a four-by-four pegboard corresponding to the location of the number on the game card. If the player can guess the correct location of all the game card numbers within eight throws of the dice, the dealer loses.
The game disclosed in the British '537 patent is challenging and somewhat educational, since it requires the player to have both sufficient knowledge of arithmetic and deductive abilities to deduce the missing numbers not revealed by the thrown dice, by subtracting the numbers revealed by the dice from the known cumulative total of the game card. However, since dice are required to initially generate up to eight of the sixteen game board numbers, these numbers are obtained by random selection, requiring no player skill. The game is also limited to play by one player, thus precluding use of this game as a group activity. Further, to my knowledge, since the game is played only with preprinted game cards, as described above, the level of difficulty involved in playing the game cannot be varied.
A numerical game testing both arithmetic and deductive abilities should be fun and challenging to adult players. More importantly, a numerical game can be a useful educational tool for teaching children basic arithmetic (e.g. addition and subtraction) operations and to aid in proper development of deductive abilities. To accomodate players of different skill, the level of difficulty during play is preferably changeable so that the game can be both challenging and educational to players of many skill levels. Finally, a numerical game is desirably capable of play as a group activity, to provide a sense of competitive awareness and to allow plural players to participate.